ESTIMATION OF WEIBULL BRITTLE-FRACTURE PARAMETERS FOR HETEROGENEOUS MATERIALS

Brittle fracture of heterogeneous materials such as dry soil aggregate s is not well understood. The flaws in such materials occur as voids a cross a wide range of length scales. As a result, failure is an inhere ntly variable phenomenon that is best analyzed using weakest-link (Wei bull) theory combined with fractal geometry. According to this probabi listic approach, samples to be fractured are assumed to be exactly the same size. However, sample size variation can result in biased estima tes of the model parameters, log(alpha), beta, and D. Our objective wa s to derive and test an equation for eliminating this bins by adjustin g survival probabilities to a common value of sample length. Rupture e nergies were determined on 1920 air-dry soil peds collected from three long-term tillage treatments on a Maury silt loam (fine, mixed, mesic Typic Paleudalf). Following adjustment for sample size variation, cha racteristic strength, as parameterized by log(alpha), typically decrea sed with increasing ped size. Unbiased estimates of beta indicated a w ider spread of strengths than reported previously. Unbiased estimates of D, the fractal scaling parameter, mere loser than those obtained us ing other methods, possibly because of renormalization with respect to the distribution of fragile elements instead of voids. Tillage treatm ent significantly influenced all three parameters, with the strength o f no-till peds decreasing more rapidly with increasing size than conve ntional-till peds. Analysis of the relative errors associated with par ameter estimates computed using the adjusted survival probabilities in dicated that at least 20 samples per sieved fraction should be used as a standard in future brittle fracture studies on heterogeneous materi als.